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If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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Question Stats: 61% (01:26) correct 39% (01:30) wrong based on 273 sessions

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If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow
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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow

From Stmt 1) y=3,then x^2-9=27=> x^2=36
=>x=6 or -6
then (x+y)^2 will be (6+3)^2=81 or (-6+3)^2=9
Hence not sufficient

From Stmt 2) (x-y)=3 and x^2-Y^2=27
=>(x-y)(x+y)=27
=>(x+y)=9
=>(x+y)^2=81
Hence Stmt 2 alone is Sufficient
Ans B
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If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3
(2) x - y = 3

Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 36
So, EITHER x = 6 OR x = -6
Let's test each case:
Case a: x = 6 and y = 3. So, (x + y)² = (6 + 3)² = 9² = 81. So, in this case, the answer to the target question is (x+y)² = 81
Case b: x = -6 and y = 3. So, (x + y)² = (-6 + 3)² = (-3)² = 9. So, in this case, the answer to the target question is (x+y)² = 9
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is (x+y)² = 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Originally posted by GMATPrepNow on 24 Jan 2018, 15:40.
Last edited by GMATPrepNow on 02 Sep 2019, 07:24, edited 1 time in total.
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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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GMATPrepNow wrote:
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3
(2) x - y = 3

Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 18
So, EITHER x = √18 OR x = -√18
Let's test each case:
Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²
Case b: x = -√18 and y = 3. So, (x + y)² = (-√18 + 3)². So, in this case, the answer to the target question is (-√18 + 3)²
NOTE: We need not actually calculate the values of (√18 + 3)² and (-√18 + 3)². We need only see that the two values are DIFFERENT
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

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Senior Manager  Status: 1,750 Q's attempted and counting
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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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Official Explanation

- First, recognize that x^2 - y^2 = (x + y)(x - y). That makes the expression a little more similar to what we're looking for -- both this and (x + y)^2 contain a (x + y) term.

Statement (1) is insufficient. If y = 3, then x^2 - 9 = 27, so x^2 = 36. x must be either 6 or -6. If x = 6, the answer is (6 + 3)^2 = 81, but if x = -6, the answer is (-6 + 3)^2 = 9.

Statement (2) is sufficient. Since (x + y)(x - y) = 27, if (x - y) = 3, then (x + y) = 9. We're looking for (x + y)^2, which is 9^2 = 81. Choice (B) is correct.
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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow

x^2 - y^2 = 27 OR (x+y)(x-y) = 27
We need to find (x+y)^2, for which we need (x+y). Here various cases are possible for (x+y) and (x-y).. Eg, former could be 9 and latter 3 or former could be 3 and latter 9 or former could be -3 and latter -9.

(1) y=3. Substituting this we get
x^2 - 3^2 = 27 OR x^2 = 27+9=36. Two values are possible for x here: 6 and -6, this will give two different answers for x+y. So Insufficient

(2) x-y=3. Substituting this we get
(x+y)*3 = 27 or x+y =9. So we can get (x+y)^2. Sufficient.

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GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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Analyzing the question:
To figure out $$(x + y)^2$$ we only need $$x + y.$$ Since we are given $$x^2 - y^2 = (x - y)(x + y) = 27$$, knowing $$x - y$$ would also give $$x + y$$ from that equation. Therefore we are trying to find $$x - y$$, $$x + y$$, or both values of x and y.

Statement 1:
(1) This gives us $$x^2 = 36$$ but we don’t know if x is positive or negative. The two solutions give different values of $$(x + y)^2$$ so this is insufficient.

Statement 2:
(2) As stated above this is sufficient.

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Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

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Top Contributor
ankitiofs wrote:
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

Posted from my mobile device

I have edited my response accordingly.

Cheers,
Brent
_________________ Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?   [#permalink] 02 Sep 2019, 07:24
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